How to make a specific area of a soft body behave like rigid body (or vice versa)?
Although it seems impossible to make a part of the mesh like a true rigid body, but following cgslav comments I could do this to some degree by assigning the vertex group to Springs as shown below. Note that the object is a bit heavy (10kg) and that's why assigning weight 1.00 to the vertices will still result in them moving a lot. Assigning lower weight values to the object fixes this issue to some degree and that is sufficient for my work.